Quote from Geann >>

I personally will not play a character with a score below 10.  As a DM, I set the number down as low as an 8, and only one of their scores can be that low.  This allows for them to be flawed, but not tragically so.  I can't imagine a Hero starting out lower than that.

 I have only thing to say to you.

You are missing out.

Personally I dislike this.  There is something about a team where everyone is above average at everything (or maybe they have a weakness but it’s offset by them being godly at 3-4 other things

Quote from Greg >>

I think it’s a mistake to overload ability scores to force role play. If you look at them through the lense of game mechanics, they only affect doing something when a check is required. Most everyday actions don’t require checks, so it’s implied that even the lowest score is not debilitating.

If you insist someone RP to a 3, you implicitly can’t allow an 18 (at least for int/wis/cha), because only a handful of humans on the planet could actually play that.

Ability scores are a very crude abstraction that are used for resolving non trivial attempts to do things. While I wouldn’t discourage a player from role playing to a low score, I think the more interesting RP comes from the effects and interactions as they attempt and fail actions more often. 

There's a big argument elsewhere about "roll playing" high INT/WIS/CHR elsewhere on the board, the oe Geann mentioned.  There's some epic length posts about negotiating the duality of player and character that I think is a bit unnecessarily restrictive (you can't play high CHR if you aren't charismatic logic).  Ironically when that thread blew up, Ginny Di had been posting short one vids coaching how to play high INT, WIS, and CHR even if you're not necessarily a genius, hyper-mindful, or a scintillating personality.  Basically playing high iNT isn't rocket science.  Nor is playing to the low end.   

I gave my players the choice to use Std Array, Pointbuy or Rolling (under supervision ofc). And I like to roll for myself. Which has me ended up with a backup level 5 Kobold, who has a lovely WIS score of 5 (-3 mod). Critical Role's Spurt, anybody?

One player who used Point Buy was hesitant so I said. "How about we just roll once. If you like the outcome, you can take it. If not, keep the old one".

The game is more than just "Player A hates Player B because one attribute is better than under his system". The ways of fine tuning characters are endless and we all agreed on doing that after all. Works fine.

I'm new to DMing and am still in the prep stages but my plan is to allow my players to roll their stats with 4D6R1x1KH3 (4d6, reroll 1s once, keep highest 3) and if they aren't happy with the results they can take the Standard Array.

I personally like the ability to have low scores but I understand that not everybody does. I think this gives those who are like me the possibility of a stat lower than 8 but doesn't force someone who got really unlucky with their rolls to play something they're not going to enjoy.

Quote from Llethander >>

I'm new to DMing and am still in the prep stages but my plan is to allow my players to roll their stats with 4D6R1x1KH3 (4d6, reroll 1s once, keep highest 3) and if they aren't happy with the results they can take the Standard Array.

I let players roll an 'extra' stat (so the usual 4d6 and drop lowest die, but do that seven times instead of six, dropping lowest total as well.) It greatly reduced the chances of getting multiple dud ability scores.